CHOICE OF AXES

A convenient choice for the axes in the small-disturbance model is to use wind axes for the lift-force and drag-force equations (5.8,1a and c), and body axes for the remaining force and moment equations (5.8,26 and 5.8,3). For vehicles having a plane of symmetry two sets of uncoupled equations are found, the longitudinal and the lateral. Since the pitching moment equation turns out to be the same in both axis systems, the longitudinal equations are then in wind axes, and the lateral in body axes.

NOTATION FOR SMALL DISTURBANCES

The reference steady state is taken to be symmetric rectilinear flight, although the more general case can readily be handled by the same approach

(ref. 6.3). The steady-state values are denoted by subscript e (for equilibrium) and changes from them by the prefix A. Thus for example

V = Ve + AV

ф — фе + Аф

P = pe + Ap (5.10,1)

L = Le + AL
etc.

Since the steady state selected is wings-level translation, we can have at most the following nonzero reference values of the state variables:

Ve’xxe’®we’V’we (5.10,2)

All other motion and angle variables are zero in the reference state and for these the prefix A is not needed. QWe as well will be zero if the reference state is horizontal flight, as it must be when we include the variation of air density with height. However, we keep as nonzero in order to include the case of constant density within the analysis. 6W, the angle of climb, is replaced with the more common symbol y.